The fundamental gap for a class of Schrödinger operators on path and hypercube graphs

DOI10.1063/1.4878120zbMath1294.81050arXiv1403.1473OpenAlexW2025033087MaRDI QIDQ5171356

Michael Jarret, Stephen P. Jordan

Publication date: 26 July 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.1473

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (2)

Modulus of continuity eigenvalue bounds for homogeneous graphs and convex subgraphs with applications to quantum Hamiltonians ⋮ Boundary effects on eigen-problems of discrete Laplacian in lattices

Cites Work

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• An optimal Poincaré inequality for convex domains
• Some eigenvalue inequalities for a class of Jacobi matrices
• Proof of the fundamental gap conjecture
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• The quantum adiabatic optimization algorithm and local minima
• Lower Bounds of the Gap Between the First and Second Eigenvalues of the Schrodinger Operator
• Optimal Lower Bound for the Gap Between the First Two Eigenvalues of One-Dimensional Schrodinger Operators with Symmetric Single-Well Potentials
• The Eigenvalue Gap for One-Dimensional Convex Potentials
• Cauchy's Interlace Theorem for Eigenvalues of Hermitian Matrices

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